Matrix Multiplication Quiz

let A be a matrix of 1 x 5 and B be matrix of 5 x 3 .

A=\begin{bmatrix} 0.6 &-15 &2&5&98\end{bmatrix}

B=\begin{bmatrix} 2&2&-4\\ 9 &-14 &0\\13&-0.5&44\\1&9&4\\0&0&5\end{bmatrix}

Notice that A is actually a row vector! A matrix with only one row or one column is a vector

A matrix with only one row is a row vector
A matrix with only one column is a column vector

If C=A x B ,

(a) How many rows will C have?

(b) How many columns will C have?

(c) What will be the value of c_{13} ?

If C=B x A ,

(d) What will be the value of c_{13} ?

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Notice that in this quiz, we multiplied a vector by a matrix, which resulted in another vector.
Essentially what happened was that our original vector, \begin{bmatrix} 0.6 &-15 &2&5&98\end{bmatrix} , went through a linear transformation and transformed into another vector with the use of the transformation matrix \begin{bmatrix} 2&2&-4\\ 9 &-14 &0\\13&-0.5&44\\1&9&4\\0&0&5\end{bmatrix} .

All this in the next set of videos.

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